Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.

4. 2 Code Segments . . . . . . . . . . . . . . . 96 4. 3 Determining Communication Parameters . 99 4. 4 Multicast Communication Overhead · 103 4. 5 Partitioning . . . . . . · 103 4. 6 Experimental Results . 117 4. 7 Conclusion. . . . . . . · 121 5 COLLECTIVE PARTITIONING AND REMAPPING FOR MULTIPLE LOOP NESTS 125 5. 1 Introduction. . . . . . . . . 125 5. 2 Program Enclosure Trees. . 128 5. 3 The CPR Algorithm . . 132 5. 4 Experimental Results. . 141 5. 5 Conclusion. . 146 BIBLIOGRAPHY. 149 INDEX . . . . . . . . 157 LIST OF FIGURES Figure 1. 1 The Butterfly Architecture. . . . . . . . . . 5 1. 2 Example of an iterative data-parallel loop . . 7 1. 3 Contiguous tiling and assignment of an iteration space. 13 2. 1 Communication along a line segment. . . 24 2. 2 Access pattern for the access offset, (3,2). 25 2. 3 Decomposing an access vector along an orthogonal basis set of vectors. . . . . . . . . . . . . . . . . . . 26 2. 4 An analysis of communication patterns. 29 2. 5 Decomposing a vector along two separate basis sets of vectors. 31 2. 6 Cache lines aligning with borders. 33 2. 7 Cache lines not aligned with borders. 34 2. 8 nh is the difference of nd and nb. 42 2. 9 nh is the sum of nd and nb. 42 2. 10 The ADAPT system. 44 2. 11 Code segment used in experiments. . 46 2. 12 Execution rates for various partitions. 47 2. 13 Execution time of partitions on Multimax. 48 2. 14 Performance increase as processing power increases. 49 2. 15 Percentage miss ratios for various aspect ratios and line sizes.